Conservation of energy - the elevator question

[jamesm113]

The cable of a 3750 lb elevator in the figure below snaps when the elevator is at rest at the first floor so that the bottom is a distance d = 12.0 ft above a cushioning spring whose force constant is k = 10,000 lb/ft. A safety device clamps the guide rails, removing 1000 ft-lb of mechanical energy for each 1.00 ft that the elevator moves.

(a) Find the speed of the elevator just before it hits the spring. mgh-1000h=mv^2/2 - 3750(12)-1000(12) = (3750/32)v^/2

v= 23.7318

(b) Find the distance that the spring is compressed. I got 2.8587 ft for this, but apparently it's wrong. Here's what I did:

mv^2/2 + mgx - 1000x = 1/2kx^2
(3750/32)(23.7318^2)/2 + 3750x - 1000x = 10000x^2/2
33000 + 2750x = 5000x^2
x= 2.8587

 

[Hootenanny]

mv^2/2 + mgx - 1000x = 1/2kx^2
(3750/32)(23.7318^2)/2 + 3750x - 1000x = 10000x^2/2
33000 + 2750x = 5000x^2
x= 2.8587

Perhaps, you forgot to multiply by 'g'?

 

[jamesm113]

3750 lbs. = mg, right?

 

[Doc Al]

Your answers (and method) look OK to me. What makes you think it's wrong?

 

[jamesm113]

I use webassign, a web based homework system and I entered the answer and it said I was wrong.

 

[Doc Al]

Often those systems are picky about the number of significant figures. Does it tell you why your answer is wrong?

 

[jamesm113]

no, and this one gives an error margin of 1%. I've never had sig fig problems before.

 

[Hootenanny]

3750 lbs. = mg, right?

Ahh yes, I forgot your in pounds. Being a Brit, I'm used to working in kilos and rarely have to deal with lbs. As Doc Al says, I can't see anything wrong with your method. Does webassign allow your to enter exact solutions? In which case the exact solution would be;

$$x = \frac{1}{40}\left( 11 + \sqrt{10681} \right)\; m$$

 

[Saketh]

If you didn't make a significant figures mistake, then the only problem could be an incorrectly entered solution by the instructor. Perhaps he accidentally entered the negative root from the quadratic function instead of the positive root. I am convinced that it is not your mistake.